chAPTER 8 POST OPTIMALITY ANALYSIS
CHAPTER 8: POST OPTIMALITY ANALYSIS
What is Post Optimality Analysis? Post Optimality Analysis Sensitivity Analysis What-If Analysis what happens to the optimal solution if THE INPUTS CHANGE THE CONDITIONS OF THE BUSINESS OBJECTIVE CHANGE THE FACTORY PARAMETERS CHANGE
What is Post Optimality Analysis? Post Optimality Analysis – Sensitivity Analysis – What-If Analysis what happens to the optimal solution if: – THE INPUTS CHANGE: – THE CONDITIONS OF THE BUSINESS OBJECTIVE CHANGE – THE FACTORY PARAMETERS CHANGE
◆ Example Let X= the number of Tables made per week Let Y= the number of chairs made per week Maximise Profit=4X+3Y Objective Function Subject to 4X+1Y≤90 Wood 2X+1Y≤50 Machine-Time 1X+1Y<40 Polishing-Time XY≥0
Example – Let X = the number of Tables made per week, Let Y = the number of Chairs made per week, – Maximise Profit = 4X + 3Y Objective Function Subject to 4X+1Y 90 Wood 2X+1Y 50 Machine-Time 1X +1Y 40 Polishing-Time X, Y 0
10 0∞元 WOOD CONSTRAINT MACHINE TIME CONSTRAINT ASE户G POLLSHING TIME CONSTRAINT No, Tables
Shadow Costs, Binding Non-Binding Constraints ◆ Wood constraint 4X+1Y<90 Optimal Solution(X, Y)=(10, 30), the wood used 4 10+1 30=70 kilograms 20 kilograms unused---slack value Let rhs90→90+1or90-1 The optimal solution does not change The addition or removal of one kilogram of Wood makes no difference to the optimal production plan. The Wood constraint is said to be a Non-Binding constraint
Shadow Costs, Binding & Non-Binding Constraints Wood constraint – 4X + 1Y 90 – Optimal Solution(X,Y)=(10,30), – the wood used 4*10+1*30=70 kilograms – 20 kilograms unused---slack value – Let RHS 90 → 90+1 or 90-1 – The optimal solution does not change. – The addition or removal of one kilogram of Wood makes no difference to the optimal production plan. The Wood constraint is said to be a Non-Binding constraint